This invention relates to a data-processing system for processing discrete data, such as digital image data, and, in particular, to a data-processing system which processes raw data to obtain data comprised of discrete data having a density different from the raw data, through the data interpolation at the time of, for example, an image enlarging processing.
Consideration will now be given to the process for interpolating and enlarging digital image data in a two-dimensional array.
In the conventional data-processing system it is common to subject data to a linear interpolation processing as in the image enlarging processing.
The linear interpolation processing is the procedure for determining interpolation data on an intermediate data point between or among data points in accordance with the geometric array of one raw data relative to one or a plurality of data adjacent to the raw data, assuming that various data are distributed in a linearly varying fashion between the data points of the raw data. That is, with values y1 and y2 known for two data points x1 and x2 use is made of an expression: EQU y=y1+(y2-y1)(x-x1)/(x2-x1)
an approximation of the value y with respect to an arbitrary point x of: EQU x.ltoreq.x.ltoreq.x2
In the data-processing system, noise components are normally contained in input data, i.e., raw data. With the linear interpolation so performed, the ratio of the noise components in the processed data depends upon the data position, and is not uniform. As a result, due to the nonuniform distribution of noise components in the processed data and hence a regular distribution obtained with respect to the data position, artifacts occur in the output image data emerged.
This will be explained below in connection with FIGS. 1 to 3.
For convenience in explanation, the interpolation processing of an interpolation ratio .mu. is here referred to as an interpolation processing whereby data d is prepared, as a .mu.:.nu. ratio (.mu.+.nu.=1), on an interior division point p between data points p1 and p2 of raw data d1 and d2. Raw data usually contains noises and, in this case, the noise of interpolated data (processed data) obtained through the linear interpolation is assumed to be of a normally distributed noise for a variance .sigma..sup.2. In this case, the interpolated data (processed data) d obtained through the linear interpolation is considered as having a variance (.mu..sup.2 +.nu..sup.2).sigma..sup.2. Since the variance as defined above can be expressed as the square root of the variance, if the variance of the noise of raw data d1, d2 is assumed to be .sqroot..sigma..sup.2 , then the noise at the data d which is obtained from raw data d1 and d2 through the linear interpolation becomes .sqroot.(.mu..sup.2 +.nu..sup.2).sigma..sup.2, which is .sqroot..mu..sup.2 +.nu..sup.2 time the raw data.
Here, when in general the interpolation ratio at the time of an enlarging interpolation processing varies depending upon the data position, the data (processed data) after interpolation has a dispersion in accordance with the variance (.mu..sup.2 +.nu..sup.2).sigma..sup.2. As a result, this nonuniform dispersion produces an undesired regular pattern, and thus artifacts are produced on emerging image data in a lattice-like pattern as shown in FIG. 3.
In the conventional data processing system utilizing the linear interpolation, the noise components of the processed data upon an enlarging interpolation has a nonuniform distribution so that artifacts are produced on the output data obtained.